Question

The solution of the equation (3y - 2) dx - (3x + 7) dy = 0 is ______

विकल्प

• `(3y + 2)/(3x + 7) = c`

• `(3y + 2)/(3x - 7) = c`

• `(3x + 7)/(3y - 2) = c`

• `(3x + 7)/(3y + 2) = c`

Answer 1

The solution of the equation (3y - 2) dx - (3x + 7) dy = 0 is `underline((3x + 7)/(3y - 2) = c)`.

Explanation:

(3y - 2) dx - (3x + 7) dy = 0 

integrating on both sides, we get

`intdx/(3x + 7) - intdy/(3y - 2) = logc_1`

⇒ `1/3log(3x + 7) - 1/3log(3y - 2) = logc_1`

⇒ log(3x + 7) - log(3y - 2) = 3 logc₁

⇒ `log((3x + 7)/(3y - 2)) =  logc_1^3`

⇒ `(3x + 7)/(3y - 2) = c`, where c = `c_1^3`